Semidefinite Characterization and Computation of Real Radical Ideals

For an ideal $I\subseteq\mathbb{R}[x]$ given by a set of generators, a new semidefinite characterization of its real radical $I(V_\mathbb{R}(I))$ is presented, provided it is zero-dimensional (even if $I$ is not). Moreover we propose an algorithm using numerical linear algebra and semidefinite optimization techniques, to compute all (finitely many) points of the real variety $V_\mathbb{R}(I)$ as well as a set of generators of the real radical ideal. The latter is obtained in the form of a border or Gr\"obner basis. The algorithm is based on moment relaxations and, in contrast to other existing methods, it exploits the real algebraic nature of the problem right from the beginning and avoids the computation of complex components.Comment: 41 page

Hadronization properties of b quarks compared to light quarks in e+e- -> q qbar from 183 to 200 GeV

The DELPHI detector at LEP has collected 54 pb^{-1} of data at a centre-of-mass energy around 183 GeV during 1997, 158 pb^{-1} around 189 GeV during 1998, and 187 pb^{-1} between 192 and 200 GeV during 1999. These data were used to measure the average charged particle multiplicity in e+e- -> b bbar events, _{bb}, and the difference delta_{bl} between _{bb} and the multiplicity, _{ll}, in generic light quark (u,d,s) events: delta_{bl}(183 GeV) = 4.55 +/- 1.31 (stat) +/- 0.73 (syst) delta_{bl}(189 GeV) = 4.43 +/- 0.85 (stat) +/- 0.61 (syst) delta_{bl}(200 GeV) = 3.39 +/- 0.89 (stat) +/- 1.01 (syst). This result is consistent with QCD predictions, while it is inconsistent with calculations assuming that the multiplicity accompanying the decay of a heavy quark is independent of the mass of the quark itself.Comment: 13 pages, 2 figure

Search for supersymmetric particles in scenarios with a gravitino LSP and stau NLSP

Sleptons, neutralinos and charginos were searched for in the context of scenarios where the lightest supersymmetric particle is the gravitino. It was assumed that the stau is the next-to-lightest supersymmetric particle. Data collected with the DELPHI detector at a centre-of-mass energy near 189 GeV were analysed combining the methods developed in previous searches at lower energies. No evidence for the production of these supersymmetric particles was found. Hence, limits were derived at 95% confidence level.Comment: 31 pages, 14 figure

Measurement of the gluon fragmentation function and a comparison of the scaling violation in gluon and quarks jets

The fragmentation functions of quarks and gluons are measured in various three-jet topologies in Z decays from the full data set collected with the Delphi detector at the Z resonance between 1992 and 1995. The results at different values of transverse momentum-like scales are compared. A parameterization of the quark and gluon fragmentation functions at a fixed reference scale is given. The quark and gluon fragmentation functions show the predicted pattern of scaling violations. The scaling violation for quark jets as a function of a transverse momentum-like scale is in a good agreement with that observed in lower energy e+e− annihilation experiments. For gluon jets it appears to be significantly stronger. The scale dependences of the gluon and quark fragmentation functions agree with the prediction of the DGLAP evolution equations from which the colour factor ratio CA/CF is measured to be: CACF=2.26±0.09stat.±0.06sys.±0.12clus.,scale

Measurement of Trilinear Gauge Couplings in e+e−e^+ e^- Collisions at 161 GeV and 172 GeV

Trilinear gauge boson couplings are measured using data taken by DELPHI at 161~GeV and 172~GeV. Values for $WWV$ couplings ($V=Z, \gamma$) are determined from a study of the reactions \eeWW\ and \eeWev, using differential distributions from the $WW$ final state in which one $W$ decays hadronically and the other leptonically, and total cross-section data from other channels. Limits are also derived on neutral $ZV\gamma$ couplings from an analysis of the reaction \eegi

Study of B0_s anti-B0_s oscillations and B0_s lifetimes using hadronic decays of B0_s mesons

Oscillations of B0s mesons have been studied in samples selected from about 3.5 million hadronic Z decays detected by DELPHI between 1992 and 1995. One analysis uses events in the exclusive decay channels: B0s -> Ds- pi+ or Ds- a1+ and B0s -> anti-D0 K- pi+ or anti-D0 K- a1+, where the D decays are completely reconstructed. In addition, B0s anti-B0s oscillations have been studied in events with an exclusively reconstructed Ds accompanied in the same hemisphere by a high momentum hadron of opposite charge. Combining the two analyses, a limit on the mass difference between the physical B0s states has been obtained: Delta(m_B0s) > 4.0 ps^{-1} at the 95% C.L. with a sensitivity of Delta(m_B0s) = 3.2 ps^{-1}. Using the latter sample of events, the B0s lifetime has been measured and an upper limit on the decay width difference between the two physical B0s states has been obtained: tau(B0s) = 1.53^{+0.16}_{-0.15}(stat.) +/- {0.07}(syst.) ps \Delta\Gamma(B0s)/\Gamma(B0s) < 0.69 at the 95% C.L. The combination of these results with those obtained using Ds+- lepton-+ sample gives: Delta(m_B0s) > 4.9 ps^{-1} at the 95% C.L. with a sensitivity of Delta(m_B0s) = 8.7 ps^{-1}. tau(B0s) = 1.46 +/- 0.11 ps and \Delta\Gamma(B0s)/\Gamma(B0s) < 0.45 at the 95% C.L.Comment: 42 pages, 13 figure

Measurement of the Mass of the Z-Boson and the Energy Calibration of Lep

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Measurement and interpretation of fermion-pair production at LEP energies from 130 to 172 GeV

The data collected with the DELPHI detector at centre-of-mass energies between 130 and 172 GeV, during LEP operation in 1995 and 1996, have been used to determine the hadronic and leptonic cross-sections and leptonic forward-backward asymmetries. In addition, the cross-section ratios and forward-backward asymmetries for flavour-tagged samples of light (uds), c and b quarks have been measured. No significant deviations from the Standard Model expectations are found. The results are interpreted by performing S-matrix fits to these data and to the data collected previously at the energies near the Z(0) resonance peak (85-93 GeV). The results are also interpreted in terms of physics beyond the Standard Model: contact interactions, R-parity violating SUSY particle exchange and of possible Z' bosons

Search for the sgoldstino at s**(1/2) from 189-GeV to 202-GeV

A search for the supersymmetric partner of the goldstino, the sgoldstino S, at LEP2 is presented. The production Sgamma followed by S decay into two gluons or into two photons was studied at 189 - 202 GeV LEP centre-of-mass energies. No evidence for the S production was found and limits on the S mass corresponding to different theory parameters are given.Comment: 15 pages, 7 figure